"Aogi" is second person feminine. It is used when it is about the person you are talking to and if the person is a female. "Ayegi" is used for third person feminine-when you are talking about a third person who is female
I got this as a "fill in the black" question. I chose the wrong verb, but the response was in red with a big x, but also "Good! Meaning..." which appears to be the response to a correct answer. I don't know how to report such a flaw.